L-moments of the Generalized Pareto Distribution

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Description

This function estimates the L-moments of the Generalized Pareto distribution given the parameters (ξ, α, and κ) from pargpa. The L-moments in terms of the parameters are

λ_1 = ξ + \frac{α}{κ+1} \mbox{,}

λ_2 = \frac{α}{(κ+2)(κ+1)} \mbox{,}

τ_3 = \frac{(1-κ)}{(κ+3)} \mbox{, and}

τ_4 = \frac{(1-κ)(2-κ)}{(κ+4)(κ+3)} \mbox{.}

Usage

1
lmomgpa(para)

Arguments

para

The parameters of the distribution.

Value

An R list is returned.

lambdas

Vector of the L-moments. First element is λ_1, second element is λ_2, and so on.

ratios

Vector of the L-moment ratios. Second element is τ, third element is τ_3 and so on.

trim

Level of symmetrical trimming used in the computation, which is 0.

leftrim

Level of left-tail trimming used in the computation, which is NULL.

rightrim

Level of right-tail trimming used in the computation, which is NULL.

source

An attribute identifying the computational source of the L-moments: “lmomgpa”.

Author(s)

W.H. Asquith

References

Hosking, J.R.M., 1990, L-moments—Analysis and estimation of distributions using linear combinations of order statistics: Journal of the Royal Statistical Society, Series B, v. 52, pp. 105–124.

Hosking, J.R.M., 1996, FORTRAN routines for use with the method of L-moments: Version 3, IBM Research Report RC20525, T.J. Watson Research Center, Yorktown Heights, New York.

Hosking, J.R.M., and Wallis, J.R., 1997, Regional frequency analysis—An approach based on L-moments: Cambridge University Press.

See Also

pargpa, cdfgpa, pdfgpa, quagpa

Examples

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lmr <- lmoms(c(123,34,4,654,37,78))
lmr
lmomgpa(pargpa(lmr))

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